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Dirac cohomology and
orthogonality relations for weight modules
Jing-Song Huang and Wei Xiao |
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Vol. 319 (2022), No. 1, 129–152
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Abstract |
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The Schur orthogonality relations for finite-dimensional representations are generalized to weight modules of complex reductive Lie algebras by establishing the equality of the Euler–Poincaré pairing and the spinor pairing. We also show how to calculate these pairings by using Dirac cohomology. |
Keywords
Dirac cohomology, weight module, Euler–Poincaré pairing,
spinor pairing
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Mathematical Subject Classification
Primary: 17B10
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Milestones
Received: 16 March 2022
Revised: 27 May 2022
Accepted: 4 June 2022
Published: 28 August 2022
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Authors |
| Jing-Song Huang | |
| School of Science and
Engineering Chinese University of Hong Kong Shenzhen China |
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| Wei Xiao | |
| College of Mathematics and
Statistics Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen University Shenzhen China |
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